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Multiplying Fractions

Multiply fractions by multiplying numerator by numerator and denominator by denominator. No common denominator needed.

Last updated: 2 December 2025

β˜…β˜…β˜†β˜†β˜† Level 2FractionsNumeratorDenominator3 min read

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The Rule

Multiplying fractions is straightforward β€” multiply top by top, bottom by bottom.

Fraction Multiplication

abΓ—cd=aΓ—cbΓ—d\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}

No common denominator needed!

23Γ—45=2Γ—43Γ—5=815\frac{2}{3} \times \frac{4}{5} = \frac{2 \times 4}{3 \times 5} = \frac{8}{15}

Cross-Cancelling (Simplify First)

You can simplify before multiplying to keep numbers small.

49Γ—38=419Γ—382=1Γ—39Γ—2=318=16\frac{4}{9} \times \frac{3}{8} = \frac{\cancel{4}^1}{9} \times \frac{3}{\cancel{8}^2} = \frac{1 \times 3}{9 \times 2} = \frac{3}{18} = \frac{1}{6}

Tip Cross-cancel between any numerator and any denominator β€” not just within the same fraction.

Multiplying a Fraction by a Whole Number

Treat the whole number as a fraction over 1:

3Γ—27=31Γ—27=673 \times \frac{2}{7} = \frac{3}{1} \times \frac{2}{7} = \frac{6}{7}

Mixed Numbers

Convert mixed numbers to improper fractions first:

212Γ—113=52Γ—43=206=103=3132\frac{1}{2} \times 1\frac{1}{3} = \frac{5}{2} \times \frac{4}{3} = \frac{20}{6} = \frac{10}{3} = 3\frac{1}{3}

Find 3/5 of 25

"Of" means multiply:

35Γ—25=3Γ—255=755=15\frac{3}{5} \times 25 = \frac{3 \times 25}{5} = \frac{75}{5} = 15

Real-World Applications

Real world: scaling down a recipe

A cake recipe serves 8 and needs 34\dfrac{3}{4} cup of butter. You want to make half the recipe (for 4 people). How much butter do you need?

12Γ—34=38\dfrac{1}{2} \times \dfrac{3}{4} = \dfrac{3}{8} cup of butter.

Real world: double discount

A jacket costs €120. A seasonal sale takes 14\dfrac{1}{4} off, then a loyalty discount takes a further 13\dfrac{1}{3} off the reduced price.

After first discount: 120Γ—34=90Β EUR120 \times \dfrac{3}{4} = 90\text{ EUR}.

After second discount: 90Γ—23=60Β EUR90 \times \dfrac{2}{3} = 60\text{ EUR}. The combined multiplier 34Γ—23=12\dfrac{3}{4} \times \dfrac{2}{3} = \dfrac{1}{2} β€” exactly half price.

Real world: calculating land area

A field is 35\dfrac{3}{5} km long and 27\dfrac{2}{7} km wide. Its area is:

35Γ—27=635Β km2\dfrac{3}{5} \times \dfrac{2}{7} = \dfrac{6}{35} \text{ km}^2

Real estate and farming use fraction multiplication whenever plots are measured as fractions of standard units.

Tip

Where do you see this? Scaling recipes, calculating stacked discounts, finding areas of fractional plots, and computing probabilities of combined events all use fraction multiplication.

Practice Problems

Calculate 3/4 Γ— 8/9.

Show answer
Cross-cancel: 3 and 9 share factor 3, 4 and 8 share factor 4. Result = 1/1 Γ— 2/3 = 2/3.

What is 2/3 of 60?

Show answer
2/3 Γ— 60 = 120/3 = 40.